Abstract: In this paper the problem of artificial neural network model is studied. The differential equation of an artificial neural network model is solved by solving a simple one imension differential equation. Applying the solution of the neural network model, we proved that all solutions of a network from the unit hypersphere over Rn converge to the origin or a point in the sphere, when all of A's eigenvalues are less than or equal to zero as well as not all of the eigenvalues equal to zero.